A numerical method for solving the                                                   Navier-Stokes equations with application to                                                   shock-boundary layer interactions

MacCormack, Robert W.; Baldwin, B. S.

doi:10.2514/6.1975-1

Cited by 167 publications

(56 citation statements)

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“…As discussed in Section 2.4.2, Peraire's finite element artificial dissipation method Peraire et al, 1988) was derived from a modified form of MacCormack and Baldwin's (1975) artificial viscosity. This dissipation method behaved satisfactorily with the PCICE-FEM scheme for all flow regimes.…”

Section: Peraire's Artificial Dissipationmentioning

confidence: 99%

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An Efficient, Semi-implicit Pressure-based Scheme Employing a High-resolution Finitie Element Method for Simulating Transient and Steady, Inviscid and Viscous, Compressible Flows on Unstructured Grids

Martineau¹,

Berry²

2003

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A new semi-implicit pressure-based Computational Fluid Dynamics (CFD) scheme for simulating a wide range of transient and steady, inviscid and viscous compressible flow on unstructured finite elements is presented here. This new CFD scheme, termed the PCICE-FEM (Pressure-Corrected ICE-Finite Element Method) scheme, is composed of three computational phases, an explicit predictor, an elliptic pressure Poisson solution, and a semiimplicit pressure-correction of the flow variables. The PCICE-FEM scheme is capable of second-order temporal accuracy by incorporating a combination of a time-weighted form of the two-step Taylor-Galerkin Finite Element Method scheme as an explicit predictor for the balance of momentum equations and the finite element form of a time-weighted trapezoid rule method for the semi-implicit form of the governing hydrodynamic equations. Second-order spatial accuracy is accomplished by linear unstructured finite element discretization. The PCICE-FEM scheme employs Flux-Corrected Transport as a high-resolution filter for shock capturing. The scheme is capable of simulating flows from the nearly incompressible to the high supersonic flow regimes.The PCICE-FEM scheme represents an advancement in mass-momentum coupled, pressurebased schemes. The governing hydrodynamic equations for this scheme are the conservative form of the balance of momentum equations (Navier-Stokes), mass conservation equation, and total energy equation. An operator splitting process is performed along explicit and implicit operators of the semi-implicit governing equations to render the PCICE-FEM scheme in the class of predictor-corrector schemes. The complete set of semi-implicit governing equations in the PCICE-FEM scheme are cast in this form, an explicit predictor phase and a semi-implicit pressure-correction phase with the elliptic pressure Poisson solution coupling the predictor-corrector phases. The result of this predictor-corrector formulation is that the pressure Poisson equation in the PCICE-FEM scheme is provided with sufficient internal energy information to avoid iteration. The ability of the PCICE-FEM scheme to accurately and efficiently simulate a wide variety of inviscid and viscous compressible flows is demonstrated here.

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Section: Peraire's Artificial Dissipationmentioning

confidence: 99%

“…It is derived from a modified form developed by MacCormack and Baldwin (1975) where the diffusion coefficient is based upon the second derivative of pressure. Peraire's main modification approximates the second derivatives with the difference between the consistent and mass-lumped matrices.…”

Section: Peraire's Artificial Dissipationmentioning

confidence: 99%

An Efficient, Semi-implicit Pressure-based Scheme Employing a High-resolution Finitie Element Method for Simulating Transient and Steady, Inviscid and Viscous, Compressible Flows on Unstructured Grids

Martineau¹,

Berry²

2003

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“…The time step is determined by considering the hyperbolic part of the system and the parabolic part of the system separately and by combining these time steps as suggested by MacCormack and Baldwin (ref. 19). The system becomes hyperbolic when viscosity is neglected.…”

Section: Time Step Limitations and Boundary Conditionsmentioning

confidence: 99%

Distributed minimal residual (DMR) method for acceleration of iterative algorithms

Lee

Dulikravich

1991

Computer Methods in Applied Mechanics and Engineering

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A new method for enhancing convergence rate of iterative algorithms for the numerical integration of systems of partial differential equations has been developed. It is termed the Distributed Minimal Residual (DMR) method and it is based on general Krylov subspace methods. The DMR method differs from the Krylov subspace methods by the fact that the iterative acceleration factors are different from equation to equation in the system. At the same time, the DMR method can be viewed as an incomplete Newton iteration method. The DMR method has been applied to Euler equations of gasdynamics and incompressible Navier-Stokes equations. All numerical test cases were obtained using either explicit four stage Runge-Kutta or Euler implicit time integration. The formulation for the DMR method is general in nature and can be applied to explicit and implicit iterative algorithms for arbitrary systems of partial differential equations.

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“…In addition, to gain computational efficiency in the normal direction to the surface (Ref. 28) the mesh is split into two or more regions. In regions where large flow gradients are anticipated, the grids describing these regions are exponentially stretched in order that acceptable numerical resolution can be achieved.…”

Section: Finite Difference Navier-stokes--deiwert Programmentioning

confidence: 99%

Calculation of Skin Friction in Two-Dimensional, Transonic, Turbulent Flow

Swafford¹

1979

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A numerical method for solving the Navier-Stokes equations with application to shock-boundary layer interactions

Cited by 167 publications

References 0 publications

An Efficient, Semi-implicit Pressure-based Scheme Employing a High-resolution Finitie Element Method for Simulating Transient and Steady, Inviscid and Viscous, Compressible Flows on Unstructured Grids

An Efficient, Semi-implicit Pressure-based Scheme Employing a High-resolution Finitie Element Method for Simulating Transient and Steady, Inviscid and Viscous, Compressible Flows on Unstructured Grids

Distributed minimal residual (DMR) method for acceleration of iterative algorithms

Calculation of Skin Friction in Two-Dimensional, Transonic, Turbulent Flow

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